Imbalanced low-rank tensor completion via latent matrix factorization.

Area of Science:

• Computer Vision
• Machine Learning
• Data Science

Background:

• Tensor completion is vital in machine learning and computer vision.
• Existing methods often assume tensors are low-rank across all modes, which real-world data may violate.
• Real-world data, like face images, can exhibit high-rank structures due to unions of low-rank subspaces.

Purpose of the Study:

• To propose an imbalanced low-rank tensor completion method.
• To address limitations of existing methods in handling real-world tensor data with complex rank structures.
• To improve the accuracy and efficiency of tensor completion.

Main Methods:

• Decomposing incomplete tensors into a mixture of multiple latent tensor ring (TR) rank components.
• Approximating each latent component using low-rank matrix factorization based on TR unfolding.
• Developing a proximal alternating minimization algorithm with proven global convergence.

Main Results:

• The proposed method achieves favorable completion results on synthetic and real-world tensor data.
• Demonstrates improved accuracy compared to state-of-the-art tensor completion methods.
• Achieves these results with reduced computational cost.

Conclusions:

• The imbalanced low-rank tensor completion method effectively handles complex tensor structures.
• The proximal alternating minimization algorithm ensures reliable convergence.
• The method offers a more efficient and accurate solution for tensor completion in practical applications.